There is little written about anything other than the roughly dozen fully detailed sectors, and the UWP generated 40 sectors or so. And much of that material isn't fully canonical.
The material in T5 was a surprise to most of the playtesters, including me. And for what its worth, aside from Marc Miller, Rob Eaglestone and Don McKinney, almost no one has any clue, and Rob and Don aren't saying.
The CT AM Zhodani notes that the Zhodani have penetrated more than 4000 parsecs coreward... (It's about 8000 parsecs to the core from Earth. 200 Sectors.)
Travellermap.com shows the Zhodani Core Route, along with a mixture of dot-map and generated map systems the whole way.
From AM4: Zhodani, p. 10.
Vlanchiets Qlom: Vlanchiets Qlom includes all Zhodani territory
beyond Chtierabl sector- approximately thirty subsector and
partial subsector-sized areas reaching 600 parsecs toward
the core. It also includes a handful of bases established by core
expeditions, some as far as halfway to the core. Portions of this
province are as much as fifty years away from Zhdant at jump-4.
There is mention of a Solomani Rimward exploration as well, but its in Solomani & Aslan, by DGP, and may no longer be canon.
The stuff that doesn't touch the 3I hasn't been defined other than what's in the T5 Rulebook, excepting, as noted, the Core Expeditions reach.
Note that some fan initiatives have generated some data on distant locations; none of which is canon, tho' some is informed by canon strongly.